Finding the Odd One Out Number Pair

The question asks us to identify the pair of numbers that does not follow the same pattern as the other pairs. To solve this, we need to look for a mathematical relationship or rule that connects the two numbers in each pair.

Analyzing Each Number Pair for Patterns

Let's examine each given pair and try to find a consistent pattern between the first number (let's call it $x$) and the second number (let's call it $y$).

Pair 1: 17 : 293

• The first number is 17.
• Let's square the first number: $\text{17}^2$.
• $\text{17}^2 = 17 \times 17 = 289$.
• The second number is 293.
• Let's see the difference between the second number and the square of the first number: $293 - 289 = 4$.
• So, for this pair, the pattern seems to be $\text{Second Number} = (\text{First Number})^2 + 4$. That is, $293 = 17^2 + 4$.

Pair 2: 19 : 365

• The first number is 19.
• Let's square the first number: $\text{19}^2$.
• $\text{19}^2 = 19 \times 19 = 361$.
• The second number is 365.
• Let's see the difference: $365 - 361 = 4$.
• For this pair, the pattern also seems to be $\text{Second Number} = (\text{First Number})^2 + 4$. That is, $365 = 19^2 + 4$.

Pair 3: 21 : 445

• The first number is 21.
• Let's square the first number: $\text{21}^2$.
• $\text{21}^2 = 21 \times 21 = 441$.
• The second number is 445.
• Let's see the difference: $445 - 441 = 4$.
• For this pair, the pattern is again $\text{Second Number} = (\text{First Number})^2 + 4$. That is, $445 = 21^2 + 4$.

Pair 4: 33 : 1097

• The first number is 33.
• Let's square the first number: $\text{33}^2$.
• $\text{33}^2 = 33 \times 33 = 1089$.
• The second number is 1097.
• Let's see the difference: $1097 - 1089 = 8$.
• For this pair, the pattern is $\text{Second Number} = (\text{First Number})^2 + 8$. That is, $1097 = 33^2 + 8$.

Identifying the Odd Pattern

We have analyzed all four number pairs:

• Pair 1 (17 : 293) follows the pattern $x^2 + 4 = y$.
• Pair 2 (19 : 365) follows the pattern $x^2 + 4 = y$.
• Pair 3 (21 : 445) follows the pattern $x^2 + 4 = y$.
• Pair 4 (33 : 1097) follows the pattern $x^2 + 8 = y$.

The first three pairs consistently follow the rule where the second number is obtained by squaring the first number and adding 4. The fourth pair follows a different rule, where 8 is added to the square of the first number instead of 4.

Therefore, the pair that is the odd one out is 33 : 1097 because it does not fit the same pattern as the other three pairs.

Based on this analysis, the pair 33 : 1097 is the odd one out.

Revision Table: Odd One Out Number Pattern

This table summarizes the pattern found for each pair in the odd one out question.

Additional Information: Solving Pattern Recognition Problems

Pattern recognition is a common type of question in reasoning and quantitative aptitude sections. To solve such problems, especially with number pairs or series, consider the following strategies:

• Look for basic arithmetic operations: Addition, subtraction, multiplication, division between consecutive numbers or within pairs.
• Check for squares or cubes: The numbers might be squares or cubes of integers, or related to them by adding or subtracting a constant.
• Prime numbers: Numbers in the sequence or pair might be prime numbers, or related to them.
• Digit properties: Sometimes the pattern involves the sum, product, or other properties of the digits of the numbers.
• Differences or ratios: Calculate the difference or ratio between consecutive terms to see if there's a pattern.
• Combination of operations: The pattern might involve multiple steps, like squaring and then adding/subtracting, or multiplying and then adding/subtracting.

Always test the hypothesized pattern with all given examples to ensure consistency before identifying the odd one out or predicting the next term.